Every square is a light, and every light is a switch. Pressing a square flips it — on becomes off, off becomes on — and flips its neighbours too.
Two facts make it a maths puzzle: pressing the same square twice puts everything back, and the order of presses doesn’t matter. So every solution is just a set of squares, each pressed once.
A good method is to “chase the lights”: for each light that is on, press the square below it, working down row by row. Whatever is left in the bottom row tells you which top-row squares to press first.
Each press flips a square and its neighbours — find the presses that switch every light off.
The full guide, with a worked example and common mistakes: How to play Light Switch.
On some boards, yes; on others (5×5 with plus-shaped switches, for example) only about a quarter of all patterns can. Every puzzle the game makes is solvable.
They mark the squares you have pressed an odd number of times — handy for spotting double presses.
The solver finds the fewest presses by solving the light equations mod 2 and trying the few free choices.
Open the Light Switch Solver, set the lights and press Solve.